Question

sin36 - sin54_____ _____sin12 sin78все в градусах

Answer 1

$\frac{sin36}{sin12}-\frac{sin54}{sin78}=\frac{sin36}{sin12}-\frac{sin(90-36)}{sin(90-12)}=\frac{sin36}{sin12}-\frac{cos36}{cos12}=\\\ \\\ =\frac{sin36*cos12-cos36*sin12}{sin12*cos12}=\frac{sin(36-12)}{sin12*cos12}=\frac{sin24}{sin12*cos12}=\\\ \\\ =\frac{2*sin24}{2*sin12*cos12}=\frac{2*sin24}{sin24}=2$